document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164995>Question 1164995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Having a difficult time with this problem...Please help!\r<BR>\n" );
document.write( "\n" );
document.write( "Solve the problem.\r<BR>\n" );
document.write( "\n" );
document.write( "A standardized math test was given to 6000 students. The scores were normally distributed with a mean of 380 and a standard deviation of 50. How many students scored between 380 and 480?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789559 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> test was given to 6000 students.<BR>\n" );
document.write( "mean was 380.<BR>\n" );
document.write( "standard deviation was 50.<BR>\n" );
document.write( "how many students scored between 380 and 480.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "doing it the easy way.<BR>\n" );
document.write( "use the calculator found at:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "enter the mean of 380.<BR>\n" );
document.write( "enter the standard deviation of 50.<BR>\n" );
document.write( "choose between.<BR>\n" );
document.write( "enter 380 to 480.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the calculator tells you that .4772 of the area under the normal distribution curve is between 380 and 480\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply 6000 by that ratio to get .4772 * 6000 = 2863.2.<BR>\n" );
document.write( "round this to 2863.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that should be your answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the hard way is a little different but should give you the same answer, or something close to it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your mean is 380 and your standard deviation is 50.<BR>\n" );
document.write( "you want to find out how many students scored between 380 and 480.<BR>\n" );
document.write( "use the z-score table to find the z-score for 380 students and the z-score for 480 students.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-score formula is z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the mean is 380.<BR>\n" );
document.write( "the standard deviation is 50.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for a raw score of 380,  the formula becomes z = (380 - 380) / 50 = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for a raw score of 480, the formula becomes z = (480 - 380) / 50 = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to to the z-score table and look for the area to the left of a z-score of 0 and to the left of a z-score of 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used the table that can be found at:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\" target = \"_blank\">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from this table, i found that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the area to the left of a z-score of 0 is equal to .5.<BR>\n" );
document.write( "the area to the left of a z-score of 2 is equal to .97725.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the area between those two z-scores is equal to .97725 minus .5 = .47725.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is actually a little more detailed than the answer given by the online calculator.<BR>\n" );
document.write( "this is because the online calculator does some rounding or truncating of the number of digits.<BR>\n" );
document.write( "because of that, the table is a little more accurate.<BR>\n" );
document.write( "but, as i said before, the answer will be close.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you now do the same thing you did before.<BR>\n" );
document.write( ".47725 * 6000 = 2863.5 which you would round off to 2863 or to 2864 according to your preference.<BR>\n" );
document.write( "remember:<BR>\n" );
document.write( "you got 2863.2 before and now you got 2863.5.<BR>\n" );
document.write( "they're pretty close and more than good enough for a rough estimate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used the z-score calculator in the TI-84 Plus and i got the following:<BR>\n" );
document.write( "m3an = 380<BR>\n" );
document.write( "standard deviation = 50<BR>\n" );
document.write( "portion of the normal distribution curve between 380 and 480 is equal to .4772499375.<BR>\n" );
document.write( "that * 6000 = 2863.499625.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is again, quite close to 2863.2 and to 2863.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, take your pick.<BR>\n" );
document.write( "you should state how you got the answer and then give the number of students you got by using that method.<BR>\n" );
document.write( "if you round up, then the answer should be 2864.<BR>\n" );
document.write( "if you round down, then the answer should be 2863.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );